Gravitational constant (G)

How to read it

Newton’s law of gravitation gives the force between two masses as G times the product of the masses, divided by the square of the distance between them (OpenStax’s University Physics writes it F⃗₁₂ = G m₁m₂/r² r̂₁₂). OpenStax calls G the universal gravitational constant: “universal” because scientists think it is the same for masses of any composition, everywhere in the Universe. A century after Newton published the law, Henry Cavendish measured G with small masses hung from a wire and larger masses placed near them, and found G = 6.67 × 10⁻¹¹ N·m²/kg². NIST lists it as the Newtonian constant of gravitation.

Also searched as: big G, G, G in physics, gravitational constant symbol, Newtonian constant of gravitation, universal gravitational constant.

Measured, not fixed

Unlike the speed of light, the elementary charge and ħ, which NIST’s table marks exact, G is still measured. NIST gives it a standard uncertainty of 0.000 15 × 10⁻¹¹ in the same units, a relative uncertainty of 2.2 × 10⁻⁵, and writes it in short as 6.674 30(15) × 10⁻¹¹, the (15) being the uncertainty in the last two digits.

G and g

Big G is a constant of nature; little g is the acceleration of a falling object near Earth’s surface, about 9.80 m/s², and depends on where you are. The two are linked: OpenStax uses g, G and Earth’s radius to work out the mass of the Earth, 5.95 × 10²⁴ kg. An upright G is the prefix giga, a billion (10⁹), as in GHz (BIPM).